The purpose of this project is to improve the remission induction rate of acute lymphocytic leukemia in adult patients utilizing vincristine and dexamethasone with intermittent moderate doses of methotrexate followed by asparaginase. A second objective is to determine whether intermittent high dose methotrexate with leucovorin rescue and with vincristine and dexamethasone will prolong remission duration. The third objective is to determine the efficacy of high dose methotrexate in preventing meningeal leukemia and to correlate the clinical effectiveness with the cerebrospinal fluid methotrexate levels. To date 38 patients have been entered onto this study. Twenty-four patients had no prior treatment, 14 had prior treatment. For the no prior treatment patients, complete remissions have been achieved in 18 of 24 (75%) patients. For the prior treatment patients, 11 of 14 (79%) achieved complete remission. The median survival for complete remission patients (no prior and prior treatment) is 18.1+ and 17.2+ months and for all patients 17.0+ and 11.2+ months respectively. Only 2 of 24 previously untreated patients (8.3%) developed CNS leukemia at 3.3 and 42.7 months from the start of therapy.